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Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:...

  1. Determine whether each of the production functions below displays constant, increasing, or decreasing returns to scale:
    1. Q = K + L + KL
    2. Q = 2K2 + 3L2
    3. Q = KL
    4. Q = min(3K, 2L)
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Answer #1

1)Q=K+L+KL

For determining returns to scale, we need to multiply the constant with both the inputs and the output.

If f(xK,xL)> xf(K,L) then it is increasing returns to scale.

If f(xK,xL)< xf(K,L), then decreasing returns to scale

If f(xK,xL)= xf(K,L)., then constant returns to scale

f(xK,xL)= xK+xL+x2KL> x(K+L+KL)=xQ

Hence this would be the case of increasing returns to scale

2) Q=2K2+3L2

f(xK,xL)= 2(xK)2+3(xL)2= x2(f(K,L)>xf(K,L)= xQ

Hence it is also giving increasing returns to scale

3)Q=KL

f(XK,xL)= (xK)(xL)= x2KL> xQ

This also displays increasing returns to scale

4)min(3K,2L)

f(xK,xL)= min(3xK,2xL)= xmin(3K,2L)= Qx

This displays constant returns to scale.

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